Details

sample215.0ms

Algorithm

intervals

Results

61.0ms	95×	body	1280	valid
44.0ms	50×	body	10240	exit
19.0ms	44×	body	640	valid
13.0ms	174×	body	80	valid
13.0ms	23×	body	1280	nan
11.0ms	193×	body	80	nan
8.0ms	30×	body	320	valid
7.0ms	20×	body	640	nan
3.0ms	11×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	9×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	252	13
5	1266	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

6.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
114.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

3 → 9

Calls

3 calls:

80.0ms	(pow x (/ 1.0 n))
191.0ms	(pow (+ x 1.0) (/ 1.0 n))
839.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

158 → 158

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	271	4785
1	740	3759
2	2874	3021
done	5002	2906

prune427.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
132.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
268.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow x (/ 1.0 n))
228.0ms	(pow (+ x 1.0) (/ 1.0 n))
367.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
417.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify2.4s

Counts

249 → 249

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	430	9019
1	929	6757
2	3222	5271
done	5000	5268

prune892.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.3b

localize42.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite594.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

152.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
138.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
130.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
139.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

408.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
444.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
741.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
699.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.8s

Counts

346 → 346

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	401	16714
1	681	12230
2	2022	9942
done	5002	8294

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.2b

localize39.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.8b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

224×	`prod-diff`
222×	`unpow-prod-down`
197×	`*-un-lft-identity`
192×	`log-prod`
183×	`cbrt-prod`
174×	`exp-sum`
144×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
67×	`sqr-pow`
30×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`log-pow` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp` `distribute-lft-out--`
1×	`flip3--` `diff-log` `flip--`

Counts

4 → 321

Calls

4 calls:

139.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
117.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
104.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
105.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

462.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
666.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
687.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
659.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify1.8s

Counts

333 → 333

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	401	16887
1	681	12419
2	2022	10111
done	5002	8343

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.2b

regimes376.0ms

Accuracy

81.2% (1.5b remaining)

Error of 22.3b against oracle of 20.8b and baseline of 28.8b

bsearch253.0ms

Steps

Iters	Range		Point
8	2.774806821063677e+19	8.926171046859927e+23	2.8287508845642576e+19
10	-2793354732730.816	-0.0035923013514488687	-73053226.23717305

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	30	71
1	39	48
done	39	48

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.6s	3070×	body	1280	valid
1.3s	1179×	body	10240	exit
1.0s	1546×	body	640	valid
971.0ms	5076×	body	80	nan
619.0ms	654×	body	1280	nan
511.0ms	4787×	body	80	valid
449.0ms	679×	body	640	nan
339.0ms	915×	body	320	valid
110.0ms	338×	body	320	nan
99.0ms	435×	body	160	valid
31.0ms	163×	body	160	nan